The Blacks Cats are without a win from their opening seven matches and currently sit bottom of the Premier League table, which in turn has made them among the favourites to be relegated.
"Everyone will say that it's going to be very difficult," he told reporters. "What I see and what I've been checking, I do believe we can get safe. I need to convince the players and everybody.
"We need to really believe in this. It's my job to make sure everyone contributes to the cause. I'm confident and I'm a positive person."
After the international break, Poyet will take charge of his first game against Swansea City.